US3005268A - Number game device - Google Patents

Description

Oct. 24, 1961 R. 5. GOLD NUMBER GAME DEVICE 3 Sheets-Sheet 1 Filed July 9, 1959 mm M0 s s IL L E S S U R 5 ATTOP/Vfy Oct. 24, 1961 R. 5. GOLD NUMBER GAME DEVICE 3 Sheets-Sheet 2 Filed July 9, 1959 INVENTOR.

Y D L O m 61,? S A L L E S S UM R Oct. 24, R. 5. GOLD NUMBER GAME DEVICE Filed July 9, 1959 3 Sheets-Sheet 5 W 308 305) E 300 v '1 w "MIMI! nmfi 3 L 322 D 71.5. 330 Bil W 32 a' W J J &x

INVENTOR.

RUSSELL S. GOLD gmQW A TTOF/VEY United States This invention concerns a device useful for education and entertainment. The device also has utility as a mathematical game for amusement and instruction of the players. When used as a game, the device may be employed to enable the operator to find a number chosen by another player or spectator and apparently not revealed by the other player to the operator.

It is one object of the invention to provide an amusement device in which a number selected by one player is determined by a second player only from information disclosed to him concerning remainders of successive divisions of the number.

It is a further object to provide a device in which there is a plurality of columns with a plurality of marked divisions in each column, the number of divisions in each column being (Bl)B where x is the ordinal number of the columns and B is the dividing number.

It is a further object to provide a game of the character described in which an indicator is provided for advancing to successive marked divisions of successive columns on a dial or chart of the game, there being a different number assigned to each mark in each division.

For further comprehension of the invention, and of the objects and advantages thereof, reference will be had to the following description and accompanying drawings, and to the appended claims in which the various novel features of the invention are more particularly set forth.

In the accompanying drawings forming a material part of this disclosure:

FIG. 1 is a plan view of a device embodying the invention.

FIG. 2 is a sectional view taken on line 22 of FIG. 1.

FIG. 3 is a plan view of another device embodying another form of the invention.

FIG. 4 is a sectional view taken on line 4-4 of FIG. 3.

FIG. 5 is a plan view of a device embodying another form of the invention.

FIG. 6 is a sectional view taken on line 6--6 of FIG. 5.

FIG. 7 is a plan view of a device embodying another form of the invention.

FIG. 8 is a plan view or" the device of FIG. 7 on an enlarged scale with portions broken away to show internal structure.

FIG. 9 is a sectional view taken on line 9-9 of used in operating the device of FIGS. 7-9.

FIGS. 1 and 2 show a circular dial D marked with a circular column or" numbers N in accordance with a system to be described. in a plurality of concentric columns I-IV are dots M. Each of the dots has a corresponding one of numbers N in radial alignment therewith as indicated by dotted lines R. A pointer or indicator P is rotatably mounted at the center or" the dial by a pin or eyelet E. This pointer has an offset portion of length P. On this portion are marked index numbers lMLJM-i located at the radial distances of columns LIV, respectively, from the center of the dial. At the outer end of the pointer is an opening W in which may be exposed any one of the numbers N as the indicator is turned around the dial.

To use the device of FIGS. 1 and 2 as a number guessing game, a player silently chooses one of the numbers N and divides that number by another arbitrary 5 atet p number B corresponding to the base of the system of numbers N. There results a whole number quotient and a remainder of either 0, l or 2, since the base B of the number system in this instance is 3. The player informs the operator of the device of the remainder and does not disclose the quotient. The operator then turns the indicator P clockwise and sets it so that index number lMl is at the first dot L1 encountered in column I it the remainder is 1, or sets it at the second dot 1-2 encountered in column I if the remainder is 2. If the remainder were 6, the operator would not move the indicator from its initial position with window W at 0 on the N numbers column as shown in FIG. 1. The player then divides the whole number quotient by 3 again and again informs the operator only of the remainder. The operator will leave the indicator in its last position if the remainder is Zero, or will move it clockwise to plate index mark 1M2 at the next encountered dot in column ll if the remainder is l, or to place index mark 1M2 at the second encountered dot in column ll if the remainder is 2. The player continues the division of quotients by 3 and the operator moves the indicator P or does not move it according to whether the remainder is 2, l or 0. After the operator locates the indicator to place the proper index mark IM at the last disclosed remainder, the indicator window W will expose therein the number N first chosen by the player.

A specific example will serve to explain the operation or" the game more clearly. Suppose the player selects number 73 in the N numbers column. He first divides 73 by the base number 3. The quotient is 24 and the remainder is l. The operator moves indicator P to place index mark 1M1 at dot 1-1 which is the first dot in the first column I. The player then divides the quotient 24 by 3 and the quotient is 8 with a remainder of O. The operator leaves the indicator at dot 1-1. The player then divides the quotient 8 by the base number 3 and the quotient of the third division is 2 with a remainder of 2. The operator then advances the indicator past dot TIL-1 to the second encountered dot ill-2 in column III which is the column to be used for the remainder of the third division. The player then divides the last quotient 2 by the base number 3, and the quotient is 0 with a remainder of 2. The operator moves the indicator to the second encountered dot IV-2 on column IV which is used for the remainder of the fourth division. Window W then will be pointing to or enclosing number 73 which is radially aligned with dot IV2.

The operation of the device may be stated more generally as follows where the device employs any base number B. First the player silently chooses a number N and divides that number by B. There results a whole number quotient Q1 and a remainder R1. The player informs the operator of the remainder and the operator advances the indicator to the dot on the first colurrm corresponding to the ordinal number of the remainder R1. The player divides the quotient Q1 by B and obtains remainder R2. The operator sets the indicator to the dot in the second column. The player repeats divisions of the quotients, and the operator each time sets the indicator to the dot corresponding to the ordinal number of the remainder in the column corresponding to the ordinal number of the division performed. When the final quotient is 0, the indicator points to the first number N selected. The operator always leaves the indicator Where it is when the remainder of a division is zero.

FIGS. 3 and 4 show another form of the game. A chart or card 200 is provided with six columns I'-VI' of dots M. Each dot or mark M has a corresponding number in transverse alignment on the card in the column VII of numbers N at one edge of the card. The

indicator 202 is a slidable member in the form of an endless band which extends transversely around the card and slides frictionally therealong. A plurality of spaced cutouts 204 are provided in the upper edge of the slider. The cutouts are numbered C1-C6 and are located so that when the slider is moved up the body of the card one of the marks M will appear in one of the' cutouts at each position of the slider. An aperture or window 206 is provided in the slider in which appears one of the numbers N at each position of the slider between the top and bottom numbers. The sequence of numbers N in column VII are arranged in accordance with a mathematical system in which the base B is 2.

The game is played with card 200 in a manner similar to the play with dial game D. Initially the slide indicator 202 is placed at in column VII. The player silently chooses a number N and divides that number by the base number 2. There results a quotient and a remainder of 0 or 1. The player informs the operator of the remainder. If the remainder is 1, the operator moves the indicatorto the first dot D-l in column I. If the remainder is zero, the operator leaves the indicator where it is; The player then divides the previous quotient by 2; There results a new quotient and a new remainder. If the remainder is 1, the operator moves the indicator to the next encountered dot in the second column II. This continues until the last quotient is 0 and there is a remainder of l. The number N selected will then appear inwindow 206. The indicator is never moved if the remainder is zero.

The game in FIGS. 5 and 6 employs dial D arranged with columns I-IV of dots M in the same manner as the game of FIG. 1. Numbers N are arranged in a circular column around the periphery of the dial. The indicator 300 is in the form of a circular disk having a sector cutout 302 of about'120. The columns I-IV are partially exposed in the cutout 302 but numbers N are wholly concealed except for a single number appearing at a rectangular'window cutout W on the periphery of the disk. The disk turns on a central pin or rivet E. Radially aligned with the pin E and the cutout W in edge 303 of cutout 302 are indentations 308 corresponding in radial position to the radial spacing of the columns I-IV. The game of FIGS. 5 and 6 is played in exactly the same manner as that of FIGS. 1 and 2, with the rotating disk taking the place of the indicator P.

In the form of the invention shown in FIGS. 7-10, the device has a dial D in which are a plurality of recesses or holes M" corresponding in position on the dial to dots M on dial D. Numbers N at the periphery of the dial are the same as numbers N on dial D. Grooves Gl-G4 in the dial are concentrically arranged and are inter-' rupted by the holes M. Holes Hl-H4 in a circular disk 320 are radially aligned and correspond in radial spacing'with that of grooves G1-G4. A cylindrical peg 322 having a rounded bottom end 324 is employed with the device. The disk 320- rotates on dial D and is held by central pin E. A cutout window W" is located in the periphery of disk 320. The numbers N are exposed in succession at the window W as the disk is rotated. A tongue 330 may be provided on dial D extending radiallybeyond disk 320 to facilitate rotation of the disk on the dial. Peg 322 is shown engaged in recess M-" in of any division is zero the disk 300 is not moved, but the peg is advanced to the next hole in the group H1-H4'. If the remainder is 2 for any division, then the peg will be lifted only enough to clear it from the first hole M" encountered in any groove and then it will be released to ride the groove until the second hole is encountered whereupon the engagement of the peg in the second hole will stop the rotation. When the last quotient is zero, the peg stops the disk at a point where the selected number N appears in window W". v

While the invention has been explained for devices employing base number 2 for that of FIGS. 3, 4 and base number 3 for thoseaof FIGS. 1, 5, 8, it is possible to employ any other base number with more or less columns of dots, marks'or holes. The mathematical basis for any arrangement of a device according to the invention is as follows. I

The general formula for the sequence S of numbers N in the numbers column is:

and a set of numbers in the sequence S of N numbers is: (YB+Z=YB +(Z1)B Where Y2B=1g ZEB, B is the base number of the system selected and x is the number of parallel columns of dots, marks or holes to be used. A set equals B numbers in the column of N numbers, consecutively positioned with the smallest number first and the largest number last.

To find numerical values of set (YB+Z) each part of S must be added to YB +(Zl)B This shall be written S The last set necessary to be found by formula is (B-l)B +'(B1)B The first B sets are found by formula. The secondB sets are found by adding to the first B sets the number 8*. The third B sets are found byv adding 23* to the first B sets. We will have then completed l/Bth of the number column. For the 2/Bth of the number col umn we add one to each of the numbers in the first l/Bth dial D corresponding to 0 in the number N column as shown at window W. a

In playing the game of FIGS. 7-10, a procedure is fol lowed as described in connection with the game of FIGS. 1 and 2. Peg 322 is placed in the first holeHl. It is lifted to clear hole M and the disk is turned while the peg rides in the first groove G1 until the first hole M" is encountered and the peg falls into the hole, if the remainder of the first division of the selected number is 1. Then the peg is placed in hole H2 and the disk is rotated again if the remainder is 1 until the peg falls into the next hole encountered in groove G2. If the remainder of the number column. For the 3/Bth of the number column we add two to each of the numbers of the first l/Bth of the number column. We continue this until for the of the number column we add B-1 to each member of v the first B numbers.

Following is an example applying the above general formula and procedure to determine the entire sequence of numbers in the circular column of numbers shown in FIG. 1:

Example In the form shown in FIG. 1, B=3. There are 81 (B numbers, one of which is 0 in the numbers column. There are four parallel columns I-IV with the marks M in the appropriate places. The marks M in the first column are placed at (0/B 360) or 0, (1/B 360) or 120, (2/B 360) or 240. In the second column 11 each sector formed by the extended adjacent radii R from column I are divided and marks M placed at l/B, 2/3 (or /3 and /3) of each sector. In the third column Hi marks M are placed /3 and /3 of each sector formed by the extended adjacent radials from columns I and II. In the fourth column IV marks M are placed at /3 and of each sector formed by the extended adjacent radii of the previous columns. Dial D has the same arrangement of holes M.

It the device had more than four columns, then in the xth column marks M Would be placed at /3 and /3 or" each sector form by the extended adjacent radii of the previous x1 columns.

While I have illustrated and described the preferred embodiments of my invention, it is to be understood that I do not limit myself to the precise constructions herein disclosed and that various changes and modifications may be made Within the scope of the invention as defined in the appended claims.

Having thus described my invention, what I claim as new, and desire to secure by United States Letters Patent 1. A mathematical device, comprising a chart having a plurality of spaced parallel columns, each of said columns being divided into a number of divisions equal to (B1)B where B is the base of a number system other than the decimal system and x is the ordinal number of the column, a plurality of numbers in the decimal system arranged in a further column outside of and parallel to said plurality of columns, the numbers in said further column while being in the base used in this column are in the sequence 0B lB 2B 35 (n1)B and an indicator movable in a predetermined direction over the chart to a plurality of positions, said indicator being provided with means for indicating one of said plurality of numbers at each of said positions, said numbers corresponding to respective marks of the divisions in said plurality of columns, said chart being a circular dial, said columns being arranged concentrically on the dial, said indicator being a disk overlaying said dial and rotatable thereon, said means being a cut-out window on said disk, said indicator having a sector cutout exposing portions of said plurality of columns while covering said further column of numbers, and a plurality of recesses formed in one edge of said sector cut-out, said recesses corresponding in spacing to the spacing of said plurality of columns.

2. A mathematical device, comprising a chart having a plurality of spaced parallel columns, each of said columns being divided into a number of divisions equal to (B-1)B where B is the base of a number system other than the decimal system and x is the ordinal number of the column, a plurality of numbers in the decimal system arranged in a further column outside of and parallel to said plurality of columns, the numbers in said further column while being in the base used in this column are in the sequence OB 1B 2B 3B (n-i)B and an indicator movable in a predetermined direction over the chart to a plurality of positions, said indicator being provided with means for indicating one of said plurality of numbers at each of said positions, said numbers corresponding to respective marks of the divisions in said plurality of columns, said chart being a circular dial, said columns being arranged concentrically on the dial, said indicator being a disk overlaying said dial and rotatable thereon, said means being a cut-out Window on said disk, said indicator having a plurality of holes disposed in spaced radial alignment between the center of the disk and said Window, the spacing of said holes corresponding to the radial spacing of said plurality of columns, said marks being further holes in said dial, and a peg removably disposed in one of the holes in said disk and engageable in one of said further holes as the disk is rotated on the dial.

References Cited in the file of this patent UNITED STATES PATENTS 1,676,410 Paul July 10, 1928 1,728,584 Wright Sept. 17, 1929 1,745,674 Hanna Feb. 4, 1930 FOREIGN PATENTS 407,078 Great Britain Mar. 12, 1934

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